Analysis

Teacher(s)

Guérit Stéphanie; Nunes Grapiglia Geovani;

Language

French

Prerequisites

Main themes

The course emphasizes:

• the understanding of mathematical tools and techniques based on a rigorous learning of the concepts favored by the highlighting of their concrete application,
• the rigorous manipulation of these tools and techniques within the framework of concrete applications.

For most of the concepts studied, the applications are chosen within the framework of the other courses of the program in computer sciences (for example biology/chemistry).

•     Sets and numbers
•     One-variable real functions
•     Boundaries
•     Continuous functions
•     Differentiable functions
•     Integrals

Learning outcomes

At the end of this learning unit, the student is able to :
S1.G1 S2.2	With regard to the AA reference system of the "Bachelor in Computer Science" program, this course contributes to the development, acquisition and evaluation of the following learning outcomes:     S1.G1     S2.2 Students who successfully complete this course will be able to:     Model concrete problems using the notions of sets, functions, limits, derivatives and integrals; Solve concrete problems using limit, derivative and integral calculation techniques; Reasoning by correctly manipulating mathematical notations and methods keeping in mind but going beyond a more intuitive interpretation of concepts.

Content

The course emphasizes:

• the understanding of mathematical tools and techniques based on a rigorous learning of the concepts favored by the highlighting of their concrete application,
• the rigorous manipulation of these tools and techniques within the framework of concrete applications.

For most of the concepts studied, the applications are chosen within the framework of the other courses of the program in computer sciences (for example biology/chemistry).
The concepts covered in this course are described below.
Sets and numbers

•     Sets (notation, intersection, union, difference)
•     Interval, upper bound, lower bound, extremum
•     Absolute value, powers and roots
•     Cardinality of a set (finite and infinite) and notion of inclusion-exclusion
•     Equivalence
•     Elements of logic and techniques of proof

One-variable real functions

•     Injective, surjective and bijective functions
•     Algebraic operations on functions (including graphical interpretation)
•     Polynomial functions
•     Exponential, logarithmic and trigonometric functions
•     Composition of functions and inverse functions

Limits and continuity

•     Conditions of existence
•     Limits to infinity
•     Fundamental theorems of continuous functions

Differentiable functions

•     Derivative at a point (including graphical interpretation)
•     Derivation techniques
•     L'Hospital's theorem
•     Maximum and minimum
•     Concavity and convexity
•     Linear function approximation
•     Taylor expansion

Primitives and integrals

•     Primitives
•     Definite integrals (including graphical interpretation)
•     Improper integrals
•     Integration techniques

First-order ordinary differential equations

Teaching methods

Lectures and exercise-based learning activities (APE). Online assignments will also be offered. The course and the learning activities through exercises will favor interactions between teachers and students.
Some of the above activities (lessons, APE, APP) can be organized remotely.

Evaluation methods

Students are assessed individually during a written exam on the basis of the learning outcomes announced above. In addition, homework results will be incorporated into the final grade as a bonus. The exact terms and conditions will be specified during the course.

Teaching materials

• Vincent Blondel, Mathématiques pour les sciences la vie - Analyse

Faculty or entity

SINC